How to find weight moving from the Earth’s core up?

1. The problem statement, all variables and given/known data
Imagine standing on a scale and riding in an elevator at constant speed in a radial direction from the center of the Earth to a distance 3RE above the surface- I’m supposed to plot weight vs time so what I’m looking for an equation(s) I can use to find weight.

*Assuming uniform desnity

2. Relevant equations
Earth Radius= 6378100 meters
*the Inverse square law 1/r^2 I think this may come into play

3. The attempt at a solution
I can find the force form gravity but I’m having a hard time deciding if I need to incorporate /how find out the decreasing mass of the Earth as I (the individual) move to the center of the Earth.
I know that at the center of the Earth the weight is 0 because the mass of the Earth is surrounding "me" and is evenly distributed…but other than that I am stuck. Help?

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